It is a nice feature of dominance solutionsĮven when dominance iteration does not lead to equilibrium, Games that are solvable by the elimination of dominated strategies are dominance solvable. Sequential elimination of dominated strategies. The solution is reached by dominance iteration, namely by the Only one strategy per player, namely (S1 s1), which is the solution to the Now both players know that S1>S2, and therefore both will In the game in table 4, neither of B’s strategies dominates We shall then say that (S2 s2) is theĪs in the game 1,1 or 2,2 are fair outcomes while dominant strategy equilibrium
To say (falsely) that S1 dominates S2, or to say that s1 dominates s2 (doesĭominant strategy, then the game has a dominanceĪre considering, S2 and s2 provide such equilibrium. Is a relation among the strategies of one player hence it does makes sense In our case, S2 strongly dominates S1, that is, S2>S1. So, a strategy Sh has always better payoffs Si if and only if E(Sh,sj)>E(Si,sj) for all sj’s. If by E(Si,sj) we understand the payoff of Consider the following (table 2) strategy matrix, where S1 and S2 areĪ brief analysis of the payoffs shows that A should adoptĪdopts, as in each box S2 has a greater payoff than S1. The simplest type of equilibrium is dominance equilibrium.
The type of equilibrium, as we shall see). (What counts as a best strategy depends on Payoff, given that the other players are playing such and such strategies. Player uses a best strategy, namely one most conducive to maximizing his The central notion for studying games is that of equilibrium, namely, a combination of strategies such that each Henceforth, unless otherwise stated, we consider only games of complete knowledge. That each player knows that all the players know this.Ī game in which such knowledge is available is a game of complete knowledge. Payoffs of each player and the strategies available to each player Since there are only 2 players, one’s winsĪre the other’s losses: the game is one of pure Game in that whatever one player wins must be lost by another player. When both A plays H and B h, A wins one penny and B loses one the box immediatelyīelow shows that when A plays T and B h, A loses his penny and B wins one. The top-left column with +1 -1 tells us that The pennies match, then A wins B’s penny (and keeps his own) if not, B winsĬan be conveniently represented by a strategy Similarly, let h be B’s strategy of playing Strategy of playing heads (placing heads up) and T that of playing tails. Consider the following game of Matching Pennies between two players A (players) who try to maximize their payoffs. Historically, game theory developed to study the strategic interactions among rational decision makers